Here is the full list of all 31 Symphony achievements. It takes around 20-25 hours to unlock all of the achievements on Windows.
St Matthew Passion, BWV 244
Play 840 minutes
"A note of shortened duration separated from the note that may follow by silence" - Find and equip the rare Sonic weapon
Symphony No. 104 in D major (Hob.I:104)
"Performing with exceptional ability, technique, or artistry" - Perfect game (100% + no death) and over 30,000 points at the Fortissimo difficulty
"Bang the piano with the fist" - Get 100% completion and over 30,000 points at the Fortissimo difficulty
"With fire / in a fiery manner" - Perfect game (100% + no death) and over 30,000 points at the Mezzo-forte difficulty
"Warlike, bellicose, belligerent or combative" - Get 100% completion and over 30,000 points at the Mezzo-forte difficulty
"Silent; do not play" - Get 0% completion
"work" or "labour"; a number generally assigned by composers to an individual composition or set of compositions on publication, to help identify their works - Finish the game
"A title of extreme respect given to a master musician" - Reach the 4-gold star rating on 10 songs
Symphony No. 5 in C minor, Op. 67 (hint: 67 is the key)
"With spirit / vigor" - Get 100% completion and over 30,000 points at the Piano difficulty
"Ignited / on fire" - Perfect game (100% + no death) and over 30,000 points at the Piano difficulty
"Always" - Reach 30,000 points and finish without dying at the Fortissimo difficulty
Unlock Fortissimo difficulty
Upgrade a weapon to level 5
Unlock Forte difficulty
"Leads a musical ensemble by way of visible gestures" - Reach the 4-Silver star rating on 10 songs
"Obstinate, persistent; a short musical pattern that is repeated throughout an entire composition" - Reach 30,000 points and finish without dying at the Mezzo-forte difficulty
Unlock Mezzo-forte difficulty
"Leader of the first violin section" - Reach the 4-bronze star rating on 10 songs
Unlock Mezzo-piano difficulty
"Sustained, lengthened" - Reach 30,000 points and finish without dying at the Piano difficulty
"A large instrumental ensemble that contains sections of string, brass, woodwind, and percussion instruments" - Equip 4 different weapons simultaneously
"A gradual increase in volume of a musical passage" - Find and equip the rare Charging weapon
Defeat the first boss
Equip a new weapon
Reach a score target
"A group of people who perform instrumental or vocal music" - Perform a 10X chain
"A group containing five members" - Perform a 5X chain